Influence of cluster shape upon its growth in a two-dimensional Ising model

Abstract

The formalism of the kinetic Ising model was used to investigate the initial growth of clusters with various number of spins and shapes in the two-dimensional Ising model on a square lattice. A general expression which provides the initial growth rate of a cluster was derived and applied to clusters of various shapes. For the simple shapes, such as rectangular, triangular, etc., the problem was treated analytically for any cluster size and expressions for the shape dependent critical size above which clusters of given shape initially grow derived. To analyze the case of arbitrary shapes, all possible configurations of clusters with up to 10 spins were generated by computer and their initial growth rate was investigated numerically. It was shown that the initial growth rate of a cluster depends not only on its size but also on the cluster shape. For a given shape there is a critical size above which the cluster initially grows. Because of this initial growth, the cluster can change its shape and will continue to grow only if its size is greater than the critical size for the new shape, and so on.